CN108732931A - A kind of multi-modal batch process modeling method based on JIT-RVM - Google Patents
A kind of multi-modal batch process modeling method based on JIT-RVM Download PDFInfo
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Abstract
The multi-modal batch process modeling method based on JIT-RVM that the invention discloses a kind of, belongs to Batch process monitoring technical field.Three-dimensional batch process historical data is unfolded and is standardized along time orientation first；Then mode division is carried out to the data after standardization using SCFCM algorithms, obtain multiple modal data subsets, instant learning is introduced in RVM, and it introduces and can calculate the data fusion similarity between real time data and historical data simultaneously from mode ownership and structure apart from the upper data fusion similarity calculation factor for evaluating data similarity；Optimization goal is finally turned to data fusion similarity maximum, establishes the optimal training dataset of instant learning, and then multi-modal batch process model is established using RVM algorithms.This method has fully considered the dynamic characteristic of batch process data, establishes the optimal training dataset of instant learning using instant learning and data fusion similarity, improves modeling accuracy.
Description
Technical field
The present invention relates to a kind of multi-modal batch process modeling methods, belong to Batch process monitoring technical field, especially relate to
And it is a kind of based on instant learning Method Using Relevance Vector Machine (Just-in-time Learning Relevance Vector Machine,
JIT-RVM multi-modal batch process modeling method).
Background technology
Batch production process is that one kind of the field of industrial production such as fine chemistry industry, biochemistry, pharmacy and food is important
The mode of production.The batch process model of high quality is established, the dynamic change of accurate description batch process is capable of, is supervised for batch process
It surveys and provides basis with optimal control.
It is traditional based on data-drivens such as pivot recurrence, Partial Least Squares Regression, artificial neural network, support vector regressions
Modeling method lacks the expression for model uncertainty, and institute's established model does not have statistical interpretation, and modeling accuracy is relatively low.It is based on
Model parameter can be considered as stochastic variable by the modeling method of Method Using Relevance Vector Machine (Relevance Vector Machine, RVM)
And prior distribution is assigned, distributed constant is modified by observing data, and the not true of model is provided by Bayesian inference
It is qualitative, so that model is had statistical interpretation, has been applied to batch process modeling, there is higher model accuracy.However, between reality
There are multiple production mode during having a rest, different modalities have different process characteristics, and containing complicated dynamic characteristic, and show
Multi-modal batch process modeling method of some based on RVM utilizes the process data training pattern of same mode so that training number
According to the invalid training data for containing part and active procedure characteristic dissmilarity is concentrated, the raising of model accuracy is constrained.
Therefore, it is necessary to be screened to historical data before modeling, extraction and the most similar history of current process data
Data establish effective training dataset.The present invention fully considers the dynamic characteristic of batch process data, introduces in RVM and learns immediately
Habit and the data fusion similarity calculation factor, establish the optimal training dataset of instant learning, improve the precision of model.
Invention content
The present invention for the purpose of improving multi-modal batch process modeling accuracy, first by three-dimensional batch process historical data along when
Between direction be unfolded and be standardized；Then fuzzy C-means clustering (the Sequence-Constrained of temporal constraint is utilized
Fuzzy C-Means, SCFCM) mode division is carried out to the data after standardization, multiple modal data subsets are obtained, in RVM
Instant learning is introduced, and introducing can be similar apart from the upper evaluation data fusion of data similarity with structure from mode ownership simultaneously
Degree calculates the factor, and it is similar to calculate the data fusion between real time data and historical data using the data fusion similarity calculation factor
Degree；Finally, Optimization goal is turned to data fusion similarity maximum, obtains the optimal training dataset of instant learning, and then utilize
RVM algorithms establish multi-modal batch process model.
The technical solution adopted by the present invention is a kind of multi-modal batch process modeling method based on JIT-RVM, this method
Specifically include following steps：
Step 1：Batch process state variable and measurand three-dimensional historical data are expanded into two-dimemsional number along variable direction
According to, then temporally direction expands into 2-D data and standardized data by status variable data in three-dimensional historical data, thus
To pretreated batch process data；
Step 2：Mode division is carried out to the pretreated batch process data that step 1 obtains using SCFCM algorithms,
Obtain multi-modal division result；
Step 3：State estimation is carried out using the mechanism model of batch process state variable, state variable is obtained and estimates in real time
It counts, according to multi-modal division result obtained by step 2, judges the affiliated mode of batch process data and its number；
Step 4：The data fusion similarity calculation factor is introduced, state variable real-time estimation data and historical data are calculated
Between similarity, extract the importation of all similar historical data and its corresponding output value part, structure instant learning is most
Excellent similar training set, establishes JIT-RVM models, finally obtains multi-modal batch process model.
Specifically, step 1 includes the following steps：
By batch process three-dimensional historic state variable dataTwo-dimensional matrix is expanded into according to time orientation
Xt(IJ1× K), wherein i is Mission Number, XiFor the status data matrix of i-th of batch, I is total batch number, J1For state
Variable number, K are total sampling time, and according to formula (1) to expanding data XtCarry out the standardization on time orientation.
In formula, mean () is data set according to the mean value on time orientation；Std () is data set according to time orientation
On standard deviation；For the data set after standardization.
By batch process state variable and measurand historical dataAccording to change
Amount direction expands into two-dimensional matrix Xv(IK×J1)、Yv(IK×J2), YiFor the measurand data matrix of i-th of batch, J2For
Measurand number provides data basis for subsequent step.
Step 2 includes the following steps：
Using track partitioning to the data set to be divided after the time is unfoldedMode thick division is carried out, is obtained
Obtain C thick division cluster centre1<C < < N；Left borderAnd subordinated-degree matrix
Wherein N is training data number, and n is data number, and c numbers for cluster centre, vcAnd bcRespectively c-th of cluster centre and its
Left margin, uc,nFor the degree of membership of n-th of training data pair, c-th of cluster centre.
It carries out SCFCM mode according to error sum of squares minimum principle using the object function of formula (2) and carefully divides.
In formula, m is fuzzy clustering index, 1≤m<∞；| | | | it is L2 normal forms.
In order to solve majorized function shown in formula (2), Lagrange multiplier is introduced, the is calculated separately using formula (3) and formula (4)
The degree of membership of k-th of cluster centre of k cluster centre and data pair, k are current cluster centre serial number.
Consider training dataset timing, introduce iteration optimal policy, read in one by one according to sequential training data and its
If after thick division as a result, training dataPreceding half-interval [b in kth classk,bk+zk/ 2], zk=bk+1-bk,zC=N-bC,
K=2,3 ..., C, the then degree of membership updated the data according to formula (5)；If training dataRear half-interval [b in kth classk+
zk/2,bk+1], zk=bk+1-bk, k=1,2 ..., C-1, then the degree of membership updated the data according to formula (6).
In formula, h numbers for cluster centre；zkFor the siding-to-siding block length of kth class.
Using formula (7) to k-th of cluster centre vkIt is updated, remembers that updated k-th of cluster centre is
Using formula (8) to the error sum of squares L of k-th of cluster centrekIt is updated, in updated k-th of the cluster of note
The error sum of squares of the heart is
Judge target error quadratic sumWhether the threshold value of setting, or update after degree of membership are less thanWith former degree of membership uc,n
Difference whether be less than a certain range, if two conditions are unsatisfactory for, re-execute formula (5) to the calculating process of formula (8), carry out
Mode updates；If there are one conditions to meet, update terminates.
Extract dataMembership vectorMiddle maximum valueAnd its serial numberMould is carried out using formula (9)
State identifies, if maximum membership degreeThen thinkBelong toMaster mode；If maximum membership degreeAnd secondary maximum
Degree of membership isOrThen think current sampleIn byToIt is a or byToA main mould
Transition mode between state.
In formula, κnFor current dataAffiliated mode serial number.
Judge whether to have traversed all training datas, if so, mode division terminates；If it is not, then reading next training
Sample, and mode division is carried out using formula (6) to formula (9), multi-modal division result is finally obtained, by Xv(IK×J1), Yv(IK
×J2) it is divided into C master mode data subset and D transition mode data subset, D=C-1.
Step 3 includes the following steps：
State real-time estimation is carried out using batch process mechanism model shown in formula (10), it is new to obtain state variable real-time estimation
Data xtest, and using mode division result obtained by step 2, obtain state variable real-time estimation data xtestAffiliated mode and its
Number κtestIf current data belongs to master mode, κ is extractedtestA master mode historical data subset；If current data is in
Transition mode, then extract κtestIt is real-time to constitute state variable for a transition mode and its adjacent two master modes historical data subset
Estimate and data xtestMode historical data subset { Xtest,Ytest}。
In formula, υ variables in order to control；η is system noise.
Step 4 includes the following steps：
In order to be found and state variable real-time estimation data x simultaneously with spatial character from process characteristictestCharacteristic close
Historical data, data modality similarity S is calculated according to formula (11) and formula (12) respectivelym,nWith data algebraic space similarity
So,n。
Sm,n=exp (- | | utest-un||2) (11)
So,n=exp (- | | xtest-xn||2) (12)
In formula, n is data sequence number；unAnd utestN-th historical data and state variable new data are subordinate to angle value respectively；
xnFor n-th of historical state data.
In order to merge two similarities, using formula (13) and formula (14) respectively to calculated data modality similarity Sm,n
With data algebraic space similarity So,nIt is standardized.
In formula,For data modality similarity set；For data modality similarity after standardization；
For data algebra space similarity set；For data algebra space similarity after standardization；For historical data number.
By the data algebra similarity after standardizationWith data modality similarityAverage value as data fusion
Similarity measure calculates the factor.
State variable real-time estimation data x is calculated using formula (15)testWith each historical state data xnBetween data fusion
Similarity Sn, obtain data fusion similarity setIn order to select the higher history number of data fusion similarity
According to as training data, important similarity discrimination threshold ζ is set, compares the data fusion similarity S of historical datanWith differentiation threshold
The size of value ζ, if historical data xnData fusion similarity SnRelationship meets formula (16) between setting discrimination threshold ζ, then it is assumed that
Data xnWith state variable real-time estimation data xtestIt is similar.
Sn≥ζ (16)
Extract all historical state data x for meeting formula (17)nAnd its corresponding measurand value yn, structure instant learning is most
Excellent training data set
Utilize the optimal training dataset of instant learningIn conjunction with RVM algorithms, JIT-RVM models are built by formula (17).
In formula, ε is that mean value is 0, variance β-1Gaussian sequence, and independently of each other；
For weight vector；For set of metadata of similar data number；For kernel function.
It is calculated using formula (18),For n-th of historical data similar with current state.
In formula, σ is gaussian kernel function width parameter.
For each weight w of modelnIt is 0 that parameter, which introduces mean value, and variance isIndependent Gaussian prior distribution, and according to formula
(19) shown in, its Posterior distrbutionp is updated using Bayes' theorem.
Σ=(β-1ΦTΦ+A) (21)
In formula, μ is weights Posterior Mean；Σ is weights posterior variance；For the hyper parameter of model,
It converts formula (19) to
Formula (22) is solved using II type maximum-likelihood method, calculates model hyper parameter, noise variance and weighting parameter
Optimal estimation valueAnd associated vector set, obtain observational variable and the JIT-RVM of state variable using formula (23)
Model.
The mechanism model g of bonding state variable finally obtains multi-modal batch process model shown in formula (24).
Advantages of the present invention：The dynamic characteristic for having fully considered batch process data introduces instant learning and data
Merge the similarity calculation factor, using the data fusion similarity calculation factor calculate batch process historical data and real time data it
Between data fusion similarity, and by maximize data fusion similarity establish the optimal training dataset of instant learning, in turn
Multi-modal batch process model is established using RVM, improves modeling accuracy.
Description of the drawings
Fig. 1 is a kind of flow chart of multi-modal batch process modeling method based on JIT-RVM of the present invention.
Fig. 2 to Fig. 4 is quantity of heat production, gas concentration lwevel in specific implementation mode under different gaussian kernel function width parameter σ
And the predicted root mean square error of pH value JIT-RVM models.
Fig. 5 to Fig. 7 is built with by traditional RVM modeling methods in specific implementation mode under JIT-RVM model optimized parameters
Prediction effect comparison diagram of the vertical RVM models for test lot 5.
Specific implementation mode
With reference to example and attached drawing, the invention will be further described, it should be noted that embodiment does not limit
The scope of protection of present invention.
Embodiment
Penicillin fermentation process is typical batch process, and Pensim emulation platforms are penicillin fed batch fermentation process
Provide the process simulation data of standard.Different primary condition are set, experimental data is generated by Pensim emulation platformsNumber of batches is I=20, and random perturbation, every batch of are added in every batch of data
Duration is 400 hours, and the sampling interval is 0.5 hour, and number of samples K=800 selects J from multiple variables1=5 shapes
State variable, J2=3 measurands, as shown in table 1.15 batches randomly choosed in 20 batches train sample as history
This, remaining 5 batches are as test data.
1 penicillin fermentation process variable declaration of table
It applies the invention in above-mentioned Modeling for Penicillin Fermentation Process, is as follows：
Step 1：By penicillin fermentation process three-dimensional state variables dataIt is unfolded according to time orientation
For two-dimensional matrix Xt(75 × 800), wherein i are Mission Number, XiFor the status data matrix of i-th of batch, and according to formula (1)
To expanding data XtCarry out the standardization on time orientation, the data set after being standardizedFor the data set after standardization；
By batch process state variable and measurand historical dataAccording to change
Amount direction expands into two-dimensional matrix Xv(12000×5)、Yv(12000 × 3), YiFor the measurand data matrix of i-th of batch,
Data basis is provided for subsequent step；
Step 2：With formula (2) for object function, first with track partitioning to the data to be divided after the time is unfolded
CollectionMode thick division is carried out, C=4 thick division cluster centre has been obtainedLeft borderAnd subordinated-degree matrix U=[uc,n](4×12000), n is data number, and c numbers for cluster centre, vcAnd bcRespectively
C cluster centre and its left margin, uc,nFor the degree of membership of n-th of training data pair, c-th of cluster centre；
The degree of membership of each cluster centre and data to each cluster centre is calculated separately using formula (3) and formula (4)；
Read in one by one according to sequential after training data and its thick division as a result, training of judgement dataIn generic
In section position, if in kth class preceding half-interval [bk,bk+zk/ 2], (zk=bk+1-bk,z4=12000-b4, k=2,3,
4) degree of membership, then updated the data according to formula (5)；If training dataRear half-interval [b in kth classk+zk/2,bk+1],
(zk=bk+1-bk, k=1,2,3), then the degree of membership updated the data according to formula (6), zkFor the siding-to-siding block length of kth class；
Using formula (7) to k-th of cluster centre vkIt is updated；
Using formula (8) to the error sum of squares L of k-th of cluster centrekIt is updated；
Judge target error quadratic sumWhether the threshold value of setting, or update after degree of membership are less thanWith former degree of membership uc,n
Difference whether be less than a certain range, if two conditions are unsatisfactory for, re-execute formula (5) to the calculating process of formula (8), carry out
Mode updates；If there are one conditions to meet, update terminates；
Extract dataMembership vectorMiddle maximum valueAnd its serial numberMould is carried out using formula (9)
State identifies；
Judge whether to have traversed all training datas, if so, mode division terminates；If it is not, then reading next training
Sample, and mode division is carried out using formula (6) to formula (9), multi-modal division result is finally obtained, by Xv(12000 × 5), Yv
(12000 × 3) are divided into C=4 master mode data subset and D=3 transition mode data subset.
Step 3：Due to Pensim platforms be based on Birol mechanism models, state variable emulation data be by
Birol mechanism models generate, therefore directly utilize mode division result obtained by step 2, to the state variable x of test lottestInto
Row mode divides, and obtains the affiliated mode of data and its number κtestIf current data belongs to master mode, κ is extractedtestA master
Mode historical data subset；If current data is in transition mode, κ is extractedtestA transition mode and its adjacent two main mould
State historical data subset constitutes mode historical data subset { Xtest,Ytest}；
Step 4：Experiment utilizes formula (11) to formula using the similarity degree between fusion similarity calculation factor S metric data
(15) test lot status data x is calculatedtestWith each historical state data xnBetween data fusion similarity Sn, counted
According to fusion similarity setFor mode historical data number；Set similarity discrimination threshold ζ=0.9, profit
Differentiate each historical state data x with formula (16)nWhether it is current state variable set of metadata of similar data.
Extract similar state data xnAnd its corresponding measurand value yn, build the optimal training data set of instant learning
Utilize the optimal similar training dataset of instant learningIn conjunction with RVM algorithms, built by formula (17) to formula (23)
JIT-RVM models.
In order to select the optimal kernel function width parameter in JIT-RVM models, one in 15 trained batches is randomly choosed
A lot data sets the variation range of gaussian kernel function width parameter σ as { δ/8, δ/4, δ/2, δ, 2 δ, 4 δ, 8 δ }, and δ is instruction
The average value for practicing each state variable standard deviation of data, brings each nuclear parameter into model successively and measures the real-time pre- of variable
It surveys, the root-mean-square error that model predication value is arranged is the evaluation index of nuclear parameter, and the smaller then model accuracy of root-mean-square error is higher,
Select the nuclear parameter with lowest mean square root error as model optimized parameter.Fig. 2 to Fig. 4 is respectively quantity of heat production, carbon dioxide
The predicted root mean square error curve graph under each nuclear parameter of concentration and pH value, table 2 are each output variable JIT-RVM models
Optimal and parameter and its corresponding root-mean-square error.
2 parameter optimization result of table
The mechanism model g of bonding state variable finally obtains multi-modal batch process model shown in formula (24).
Above-mentioned steps are the concrete application that the present invention establishes process model in penicillin fermentation process emulation platform, in order to test
Effectiveness of the invention is demonstrate,proved, multi-modal batch process modeling method of the setting based on RVM is Experimental comparison's method, is utilized respectively most
RVM models and JIT-RVM models under excellent nuclear parameter predict the process data of the measurand of test lot, and with pre-
The root-mean-square error of measured value is model-evaluation index, and table 3 is the prediction result of 5 test lots.Fig. 5 to Fig. 7 is respectively to test
The prediction effect figure of 5 each measurand of batch.
35 batch measurand predicted root mean square errors of table
It can be obtained from the prediction result of 5 batches, compared to multi-modal batch process modeling side of the tradition based on RVM
Method can be extracted accurately to build with high similar historical data based on the multi-modal batch process modeling methods of JIT-RVM and be learned immediately
Optimal training dataset is practised, and then establishes multi-modal batch process model, describes the dynamic change of process, what is obtained is multi-modal
The model prediction curve of batch process model has smaller error with Pensim simulation curves, shows the method for the invention tool
There is lower multi-modal batch process data prediction error, building multi-modal batch process model has higher model accuracy.
Claims (5)
1. a kind of multi-modal batch process modeling method based on JIT-RVM, it is characterised in that：This method specifically includes following step
Suddenly：
Step 1：Batch process state variable and measurand three-dimensional historical data are expanded into 2-D data along variable direction,
By status variable data in three-dimensional historical data, temporally direction expands into 2-D data and standardized data again, thus obtains pre-
Batch process data that treated；
Step 2：Mode division is carried out to the pretreated batch process data that step 1 obtains using SCFCM algorithms, is obtained
Multi-modal division result；
Step 3：State estimation is carried out using the mechanism model of batch process state variable, obtains state variable real-time estimation number
According to according to multi-modal division result obtained by step 2, judging the affiliated mode of batch process data and its number；
Step 4：The data fusion similarity calculation factor is introduced, is calculated between state variable real-time estimation data and historical data
Similarity, extract the importation of all similar historical data and its corresponding output value part, build the optimal phase of instant learning
Like training set, JIT-RVM models are established, finally obtain multi-modal batch process model.
2. a kind of multi-modal batch process modeling method based on JIT-RVM according to claim 1, it is characterised in that：
Step 1 includes the following steps：
By batch process three-dimensional historic state variable dataTwo-dimensional matrix X is expanded into according to time orientationt(IJ1
× K), wherein i is Mission Number, XiFor the status data matrix of i-th of batch, I is total batch number, J1For state variable
Number, K are total sampling time, and according to formula (1) to expanding data XtCarry out the standardization on time orientation；
In formula, mean () is data set according to the mean value on time orientation；Std () is data set according on time orientation
Standard deviation；For the data set after standardization；
By batch process state variable and measurand historical dataAccording to variable side
To expanding into two-dimensional matrix Xv(IK×J1)、Yv(IK×J2), YiFor the measurand data matrix of i-th of batch, J2To measure
Variable number provides data basis for subsequent step.
3. a kind of multi-modal batch process modeling method based on JIT-RVM according to claim 1, it is characterised in that：
Step 2 includes the following steps：
Using track partitioning to the data set to be divided after the time is unfoldedMode thick division is carried out, C is obtained
A thick division cluster centre1<C < < N；Left borderAnd subordinated-degree matrix U=[uc,n](C×N),
Wherein N is training data number, and n is data number, and c numbers for cluster centre, vcAnd bcRespectively c-th of cluster centre and its
Left margin, uc,nFor the degree of membership of n-th of training data pair, c-th of cluster centre；
It carries out SCFCM mode according to error sum of squares minimum principle using the object function of formula (2) and carefully divides；
In formula, m is fuzzy clustering index, 1≤m<∞；| | | | it is L2 normal forms；
In order to solve majorized function shown in formula (2), Lagrange multiplier is introduced, is calculated separately k-th using formula (3) and formula (4)
The degree of membership of k-th of cluster centre of cluster centre and data pair, k are current cluster centre serial number；
Consider the timing of training dataset, introduce iteration optimal policy, reads in training data and its thick stroke one by one according to sequential
If point after as a result, training dataPreceding half-interval [b in kth classk,bk+zk/ 2], zk=bk+1-bk,zC=N-bC, k=
2,3 ..., C, the then degree of membership updated the data according to formula (5)；If training dataRear half-interval [b in kth classk+zk/
2,bk+1], zk=bk+1-bk, k=1,2 ..., C-1, then the degree of membership updated the data according to formula (6)；
In formula, h numbers for cluster centre；zkFor the siding-to-siding block length of kth class；
Using formula (7) to k-th of cluster centre vkIt is updated, remembers that updated k-th of cluster centre is
Using formula (8) to the error sum of squares L of k-th of cluster centrekIt is updated, remembers the mistake of updated k-th of cluster centre
Poor quadratic sum is
Judge target error quadratic sumWhether the threshold value of setting, or update after degree of membership are less thanWith former degree of membership uc,nDifference
Whether it is less than a certain range, if two conditions are unsatisfactory for, re-execute formula (5) to the calculating process of formula (8), carry out mode
Update；If there are one conditions to meet, update terminates；
Extract dataMembership vectorMiddle maximum valueAnd its serial numberMode knowledge is carried out using formula (9)
Not, if maximum membership degreeThen thinkBelong toMaster mode；If maximum membership degreeAnd secondary maximum is subordinate to
Degree isOrThen think current sampleIn byToIt is a or byToBetween a master mode
Transition mode；
In formula, κnFor current dataAffiliated mode serial number；
Judge whether to have traversed all training datas, if so, mode division terminates；If it is not, next training sample is then read,
And mode division is carried out using formula (6) to formula (9), multi-modal division result is finally obtained, by Xv(IK×J1), Yv(IK×J2)
It is divided into C master mode data subset and D transition mode data subset, D=C-1.
4. a kind of multi-modal batch process modeling method based on JIT-RVM according to claim 1, it is characterised in that：
The step 3, specifically includes：
State real-time estimation is carried out using batch process mechanism model shown in formula (10), obtains state variable real-time estimation new data
xtest, and using mode division result obtained by step 2, obtain state variable real-time estimation data xtestAffiliated mode and its number
κtestIf current data belongs to master mode, κ is extractedtestA master mode historical data subset；If current data is in transition
Mode then extracts κtestA transition mode and its adjacent two master modes historical data subset, constitute state variable estimate in real time and
Data xtestMode historical data subset { Xtest,Ytest}；
In formula, υ variables in order to control；η is system noise.
5. a kind of multi-modal batch process modeling method based on JIT-RVM according to claim 1, it is characterised in that：
The step 4, specifically includes：
In order to be found and state variable real-time estimation data x simultaneously with spatial character from process characteristictestThe history of characteristic close
Data calculate data modality similarity S according to formula (11) and formula (12) respectivelym,nWith data algebraic space similarity So,n；
Sm,n=exp (- | | utest-un||2) (11)
So,n=exp (- | | xtest-xn||2) (12)
In formula, n is data sequence number；unAnd utestN-th historical data and state variable new data are subordinate to angle value respectively；xnFor
N-th of historical state data；
In order to merge two similarities, using formula (13) and formula (14) respectively to calculated data modality similarity Sm,nSum number
According to algebraic space similarity So,nIt is standardized；
In formula,For data modality similarity set；For data modality similarity after standardization；
For data algebra space similarity set；For data algebra space similarity after standardization；For historical data number；
By the data algebra similarity after standardizationWith data modality similarityAverage value it is similar as data fusion
The metric calculation factor；
State variable real-time estimation data x is calculated using formula (15)testWith each historical state data xnBetween data fusion it is similar
Spend Sn, obtain data fusion similarity setIn order to select the higher historical data of data fusion similarity to make
For training data, important similarity discrimination threshold is setCompare the data fusion similarity S of historical datanWith discrimination threshold
Size, if historical data xnData fusion similarity SnWith setting discrimination thresholdBetween relationship meet formula (16), then it is assumed that should
Data xnWith state variable real-time estimation data xtestIt is similar；
Extract all historical state data x for meeting formula (17)nAnd its corresponding measurand value yn, build the optimal instruction of instant learning
Practice data acquisition system
Utilize the optimal training dataset of instant learningIn conjunction with RVM algorithms, JIT-RVM models are built by formula (17)；
In formula, ε is that mean value is 0, variance β-1Gaussian sequence, and independently of each other；For power
Value vector；For set of metadata of similar data number； For kernel function；
It is calculated using formula (18),For n-th of historical data similar with current state；
In formula, σ is gaussian kernel function width parameter；
For each weight w of modelnIt is 0 that parameter, which introduces mean value, and variance isIndependent Gaussian prior distribution, and according to formula (19) institute
Show, updates its Posterior distrbutionp using Bayes' theorem；
Σ=(β-1ΦTΦ+A) (21)
In formula, μ is weights Posterior Mean；Σ is weights posterior variance；For the hyper parameter of model,
It converts formula (19) to
Formula (22) is solved using II type maximum-likelihood method, calculates the optimal of model hyper parameter, noise variance and weighting parameter
Estimated valueAnd associated vector set, obtain observational variable and the JIT-RVM models of state variable using formula (23)；
The mechanism model g of bonding state variable finally obtains multi-modal batch process model shown in formula (24)；
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